Gravity from Expanding Space.

[cosnut]

I will start with a simple assertion: The gravitational constant expressed as meters^3/sec^2 per kgm is equivalent to exponential cosmological acceleration per unit mass, i.e., volumetric acceleration per unit mass.

 

Starting with a Hubble sized sphere of radius R having a volume 4/3(pi)R^3, differentiate twice to get volumetric acceleration. Since the Hubble grows at constant velocity c, the volumetric acceleration for a space receding at a constant rate c is 8(pi)Rc^2. However, we are interested in the recessional rate which is believed to be accelerating - if the recessional rate is accelerating there will another term which corresponds to q = -1, that is [4(pi)R^2][d^2R/dt^2]. But this second term can be written as

4(pi)R^2 [-(c^2)q/R] and for q = -1 the total acceleration for a q = -1 universe is 12(pi)Rc^2

 

Next divide by the Hubble area 4(pi)R^2 to convert the volumetric acceleration to a surface integral. The volumetric acceleration per unit area is therefore 3(H^2)R.

 

Einstein introduced Lambda to balance gravity - he needed to have an acceleration that balanced G. (Lambda)® would balance G if Lambda equaled 3(H^2). And if Lambda equals 3(H^2), then (lambda)® is simply the cosmological volumetric acceleration of exponentially expanding space as per the above.

 

After responding to the reverberations from the members, I will complete the derivation of G by illustrating the transform from volumetric acceleration per unit area to volumetric acceleration per unit mass. At this juncture the two accelerations are equal, but of course one will say - how can a static universe be at the same time an accelerating universe?

Edited July 20, 2014 by cosnut

[Mordred]

here is one immediate problem a static universe is a closed universe, Also our observable universe is larger than the Hubble radius.

 

Einsteins static universe is only possible with a positive [latex]\Lambda[/latex] and positive curvature k=1

 

the value for [Latex]\Lambda[/Latex] in his model is [Latex]4\pi G \rho[/Latex] please note G is used here, however the static universe is unstable. This is already well known so no one will ask why the universe is expanding when the universe is static as the two are incompatible by definition

 

a static universe is a closed curved universe, this is not our universe. Our universe is flat and may or may not be closed.

http://www.astro.umd.edu/~miller/teaching/astr422/lecture12.pdf

 

the critical density formula is a perfectly flat universe. which is defined with [Latex]|\Lambda=0[/Latex] which coresponds to an average energy density of 1.88h^2*10^-29 g/cm^3

[latex]\rho_{crit} = \frac{3c^2H^2}{8\pi G}[/latex]

"The critical density is the boundary value between universe models that expand forever (open models) and those that recollapse (closed models)"

 

I have no idea where you get this q-1 term this isn't used in the FLRW metric at all

 

http://cosmology101.wikidot.com/universe-geometry

http://cosmology101.wikidot.com/geometry-flrw-metric/ page 2 of previous link

 

http://arxiv.org/pdf/hep-ph/0004188v1.pdf :"ASTROPHYSICS AND COSMOLOGY"- A compilation of cosmology by Juan Garcıa-Bellido

http://arxiv.org/pdf/hep-ph/0004188v1.pdf

 

our universe is k=0 or extremely close to it so if your q=-1 is suppose to be k=-1 then your talking about our universe

Edited July 20, 2014 by Mordred

[Strange]

After responding to the reverberations from the members...

 

Nice use of the word "reverberations"

 

I noticed that on another forum, when the members pointed out all the flaws you just walked away. It seems you don't have much confidence in the idea.

[cosnut]

Thanks for your response Mordred The theory is not confined to a closed or curved universe, I am using the Hubble sphere as a measuring gauge - space can be flat or curved within the framework of the equations.

 

I may have made a typo - I am referring the q = -1 de Sitter universe (exponential expansion at the present), I did not mean to refer to q raised to the

-1 power.

 

As will be shown subsequently, the formalism is not a decelerating universe - so the 1932 Einstein- de Sitter model is not applicable. In fact density and gravity will be shown to depend upon the expansion rate - so density always appears to have a value that corresponds to a constant c expansion rate (q = 0) In this regard, the model conflicts with the present LambdaCDM model but it doing so it eliminates the thorny problem of why the universe needs to be fine tuned to a critical density.

 

In evaluating a new theory, one is obliged to temporarily suspend judgment based upon theory extracted from models that are in conflict - this does not mean one ignores facts which are well documented. What is generally not in issue is the approximate age of the universe (14 G years, present Hubble radius about 1 x 10^26 meters, flat or nearly flat space). Interestingly, the theory of gravity from expanding space does not conflict with GR regarding curvature, but it attributes it as a consequence of the warping of the global acceleration field rather than the cause of gravity.

 

I have read many of your posts on PF, thanking you again for taking the time to reply

 

Today I will try to answer my rhetorical at the end of the first post.

[Mordred]

As will be shown subsequently, the formalism is not a decelerating universe - so the 1932 Einstein- de Sitter model is not applicable. In fact density and gravity will be shown to depend upon the expansion rate - so density always appears to have a value that corresponds to a constant c expansion rate (q = 0) In this regard, the model conflicts with the present LambdaCDM model but it doing so it eliminates the thorny problem of why the universe needs to be fine tuned to a critical density.

 

 

 

the model would not only conflict with LCDM it will also conflict with thermodyanics. a constant density will mean a constant temperature. As the universe expands the average energy=density lowers thus the temperature drops. We see this with observations. So if your model has an average constant density its temperature will always remain the same.

 

also observations show us that we can have objects with recessive velocity of 3c at z=1090

 

so lets agree this is a toy universe for the time being, in which case go ahead and present your idea's it will be easier to follow if you can latex

 

the same latex rules follow as PF but you need to type latex instead of tex this site is also more susceptible to spacing so there is a few syntax differences to get used to

Edited July 20, 2014 by Mordred

[cosnut]

I have a very strong conviction that the constants, G, q, alpha, can be derived from fundamental physics principles once the right model is discovered.

 

I tried several times to explain how to transform from Volumetric acceleration/area to volumetric acceleration/mass and finally gave up - not on the theory, but the way the discussion had proceeded with no progress. To the few who were still trying to understand without making rude comments, I offered an opportunity to download the entire theory and to correspond by email. One of the things that became very frustrating was that when drafting a detailed equation it takes some time and for whatever reason, that web site times-out too quickly and on several occasions all the effort of composing a detailed post was lost.

[Mordred]

the workaround to that is to use Office and type it all out first then copy paste, keep the formulas in how the latex would be typed

as we are talking a personal model this forum has a useful speculations section that is more open to personal models.

 

this site prefers to stay with the concordance answers in this sub forum. So as this is admittedly a non concordance model or peer reviewed then it would be more appropriate in the speculation sub forum where the rules on personal model idea's are more relaxed

Edited July 20, 2014 by Mordred

[cosnut]

I don't believe I said anything about a constant density, the density turns out to be rho = (3/R)(kgm/meters^2) where the multiplier units follow from the transform from (vol acc)/area to (vol acc)/mass which I will present shortly. Density falls off inversely with radius rather than inversely with the volume - inasmuch as mass is not constant.

 

Two things are varying at the same time - this initially sounds rather revolting - but it turns out to resolve a number of mysteries - What is verified by experiment is the constancy of the MG product - In the theory I briefly outlined in post 1, the acceleration of space corresponds to (H^2)R along any line of action, so if this is to be a basis of G, then G will be formed from c^2/R, in other works G decreases as 1/R as Dirac proposed in his LNH.

 

Now the attempts to measure G using long term studies of lunar orbits are often cited as debunking variable G - but these studies only confirm the constancy of the MG product. There is no law of conservation of mass, energy as is well known, is turned into mass during proton-proton bombardment.

 

But in the case of expanding space as the source, we are not talking about new particle creation, but rather enhanced inertia. This is then a Machian process where the amount of inertial mass grows as the universe expands.

 

So instead of trying to fit the explanation of the universe into a framework of fixed constants (G and Cosmic Mass) we incorporate two ideas that together allow Inertia and G to vary. This leads to heretofore mysteries easily explained, as will be shown subsequently.

Ok I will type, copy and paste. When I looked at the various topics I recall a lot of things that looked very controversial, like positive claims of ether and the like - so I mistakenly thought this was more flexible forum that PF.

One point - I believe your formula for rho critical has a c^2 term by mistake - you may want to correct it.

[StringJunky]

Ok I will type, copy and paste. When I looked at the various topics I recall a lot of things that looked very controversial, like positive claims of ether and the like - so I mistakenly thought this was more flexible forum that PF.

It is more flexible than PF - it has a speculations forum. It's important for the novices - including myself - to keep established science distinct from users personal ideas so that they may not become confused.

[Mordred]

the speculations section is relaxed enough for us to work on a toy universe.

 

the form I gave above is one in some books but I should give the more well known form

 

[latex]\rho_{crit} = \frac{3H^2}{8\pi G}[/latex]

Edited July 20, 2014 by Mordred

[cosnut]

Understand - this is a theory that does not fit the standard model although it does not conflict with GR per se. In fact, if it turns out to have merit, it bolsters all theories in the sense that they now depend upon G as a magic constant determined only empirically - to that extent all theories are incomplete - this doesn't seem to bother anyone since all theories are incomplete to some extent - but in the case of gravity, theory is descriptive at the point where functionality is critical to understanding.

[Mordred]

well there is certainly models with variable constants with variable G out there, several I've studied in the past. So its not a dumb idea by any means, the question is does the model conform with observations. Under the precepts of a toy model development its simply good practice to try modelling a system and see then what observational evidence would be needed to validate or invalidate the model.

 

here is a couple

Can a variable gravitational constant resolve the Faint Young Sun Paradox ?

http://arxiv-web3.library.cornell.edu/abs/1405.4369?context=astro-ph.CO

 

 

this one covers a couple of models and using data discounts them

The variation of the gravitational constant inferred from the Hubble diagram of Type Ia supernovae

http://arxiv.org/abs/gr-qc/0512164

 

also mentions the large number hypothesis LNH and the details you wrote earlier, so you may have already read this article.

 

this is however one set of findings that your going to have to work against,

 

here is other constraints

Observational constraints on models of the Universe with time variable Gravitational and Cosmological constants along MOG

 

http://arxiv.org/abs/1403.0081

this paper looks interesting but I haven't completed reading it 155 pages lol

might provide some insight as its on the same subject matter

http://relativity.livingreviews.org/Articles/lrr-2011-2/download/lrr-2011-2Color.pdf

 

models are certainly available to show varying constants, the problem is addressing the observational constraints

Edited July 21, 2014 by Mordred

[cosnut]

Thank you for the links. The first paper on the Faint Young Sun Paradox is directly in point. Of particular interest for me was the discussion which centered on the Supernova ...." a larger G value in the past would result in SN1a being fainter than predicted by the standard candle hypothesis."

 

At page 40 of my thesis, I state: "A larger Gravitational acceleration requires less mass to create the same force. Since electron degeneracy pressure is constant, less mass is required to trigger 1a supernova events"

 

As I indicated in my post, because M increases during the growth of the cosmos and G falls off as I/R per Dirac, the theory admits much greater G variance than that allowed in other theories. Most of the papers have failed to appreciate that the planetary lunar orbital data verifies the constancy of the MG product, not the constancy of G - so the theorists are unnecessarily limiting their discussion to very small changes that would not be revealed by the constancy of the lunar orbits . The faint Sun problem and the 1A super nova data are both look-back experiments to a time when the result would be different if G were large and M less. So It would seem that since the solar intensity is proportional to the 7th power of G and the fifth power of solar mass, the faint Sun paradox could easily be explained ---and without having to postulate that a greater G would have resulted in a closer orbit to the Sun as did the authors - again - orbits are not affected if the MG product is constant.

 

Is there a place on this forum where I can post a complete copy of the Thesis - I have not been able to upload selected parts successfully

[Mordred]

40 pages would be troublesome to copy paste lol, you have obviously placed a lot of time and effort into it. I look forward to being able to read it

 

 

if you click more reply options you should see the attachments icon, assuming the file is less than 1.9 MB. If you can't see the option then you may need to have more posts to enable the feature. I can't recall the number needed but I think you should have enough.

 

I can only open pdf not doc extensions. A handy converter is pdf995

http://www.pdf995.com/

its basically a printer emulator to convert any software doc/program that has a printer option into a pdf file. extremely handy.

 

if the file size is too big you might have to place it on a webpage then link it. I use wikidot for that, see signature. Its handy for the large file size articles and also gives me a means to keep track of handy help teach articles. You upload to wikidot then post a link on a page you make. Or optionally you can also set your article onto it page for page, its latex is easy to use.

http://www.wikidot.com/

Edited July 21, 2014 by Mordred

[cosnut]

The legend states a 4.8 MB file can be handled, but After trying several times to up load a one MB file covering the essentials of the First Chapter I gave up and managed to get a one page Appendix to load. I will annotate how the result were arrived at if anyone is interested, The one page summary actually takes a known planet and makes a comparison of how the model plays out - there are immediately two things that will raise questions - why is it possible to substitute one kgm per meter for the Hubble surface density. In the paper I derive the Hubble mass as 4(pi)R^2 kgm/m^2. This is approximately what one arrives at using the estimated value of 10^53 kgm for the Hubble mass and 10^26 meters for the Hubble radius, so there is some credibility for the one kgm/meter^2 surface density based upon the stand model and the estimates obtained therefrom.

 

The other fact which will arose suspicion is 5/6 correction factor - the two sphere model leads to a simple one to one relationship between the two surface areas and the two masses. But the energy of a two sphere of mass M and radius R is less than the energy of a three sphere of mass M and radius R.

The two sphere as a coefficient 1/2, the threes sphere a coefficient 3/5 - the energy difference for the same radius is thus 5/6 greater for the three sphere - so there needs to be a radial adjustment of 5/6.

 

 

Appendix II-a.pdf

[cosnut]

Readers will also note that the expression for the local g field can be reworked backwards to extract big G. Specifically, the local force acting upon a local mass rearranges as:

 

F = [(c^2)/4(pi)R][(meters^2)/kgm] x {Me/(r^2)}

 

Then calling everything underlined between the brackets 'G,' the local force is F reduces to the standard form of the gravitational force equation;

 

F = G{(Me/r^2} where e is a subscript, and r can have any value greater that the radius of the planet

 

As previously belabored, R is the radius of a two sphere universe. When adjusted by the 5/6 factor, the force corresponds to that measured for the earth and G corresponds to the measured value for a Hubble constant in the range of 71

[Mordred]

ok I've looked over this paper and taking it from a similar view point to LNH and not LCDM. The problem I see is that I don't think it will fit within the measured constraints of varying G studies.

 

Granted there are different values for a varying G, the numbers of each study is still a small change per year I'm basing my numbers of the Gong and Bison data. (keep in mind this data is also uncertain, and not strong enough to support a varying G)

 

http://iopscience.iop.org/0004-637X/498/2/871/pdf/0004-637X_498_2_871.pdf

 

based on this test the variation is +or - 1.6*10^-16 per year

 

this is a tighter constraint than the supernova data paper I posted earlier

 

G/G₀ <8.0*10^-12 per year however that paper shows the improved constraints at 10^-14

 

I don't have time to do the full data set math, so this is what I would like to see from you. Take your model crunch together a data set and see if it falls within those constraints and post the results. ( you must admit that is about as open minded of a query as one could expect of a new model)

Edited July 23, 2014 by Mordred

[cosnut]

Here is the obstacle to the present limit on the variability of G,

 

How do we test for changing G - we observe things that depend upon G, like the orbits of the moons of mars - what are we measuring

 

We set two things equal, Gravitational force = centripetal force

 

F = Mm'G/(r^2) = m'v^/r

 

Result MG = (v^2)r

 

This test like every test we can think to perform, tells us that the MG product is constant - But variable G is intimately tied to the idea of a zero energy universe. Two things are varying at the same time. The inertial property of mass which we denote by M is also the energy property we denote by M. Machian bootstrap mechanics must be in play in a zero energy universe. Dirac's LNH required that G vary as I/R. We would be able to measure 1/R changes by the drift in the orbits of planetary moons during a 5 year study, but we don't. That is because the MG product in our universe is always constant.

 

I pondered this particular problem for a long time. Eventually I found a set of equations that is internally consistent with G proportional to1/R. They are totally in agreement with some other observational peculiarities such as the ratio long studied by Robert Dicke and others as to why the ratio GM/R(c^2) = 1 within the limits of experimental error (where M is the mass of the Hubble sphere). Its a simple consequence of the fact that cosmic mass is equal to [4(pi)R^2]kgm/meter^2 and G = [c^2/4(pi)R] as derived in the attachment to my previous post.

 

So as you see, the expansion theory of gravity does not fit within the experiments that show G to be constant. But there are no such experiments. Not one. You cannot measure G by itself.

 

I am always reminded of Einstein's statement when asked to describe GR in one sentence, he responded: "Time, Space and gravitation have no separate existence from matter...."

 

There are some beautiful benefits to a theory built upon non-constants - no fine tuning is required to balance inertial mass, gravity is revealed as an emergent field, a consequence of expansion.

 

I managed to copy off another page which readers may find useful in criticizing the derivation - I will attach it in a separate post

 

Thanks again for your interest Mordred , seems you are the only one curious about the theory - if you like I will attach a copy of chapter I to an email which can read at your leisure for comic relief

Here is a page which I will try to upload for those who would like to see a more physical perspective

 

A bit of history on his subject from a personal perspective: Some years ago there was a thread on PF started by another skeptic who had the same idea that G could be derived from expanding space. His method involved writing an expression for the g force between the mass of the universe and some other mass using Newton's gravitational force equation and work backwards and solve for G. I exchanged posts with him as I had already derived my own expression for G in terms of cosmological acceleration - he used the velocity-distance law v = Hr and differentiated as I had done previously to see where it would lead. The resulting acceleration is c^2/R, but at the time the accelerating universe had not been discovered so I didn't know whether the approach would have any merit. Anyway it led to a G

 

G = 3(H^2)/4(pi)(rho)

 

where rho is the average cosmic density

 

After revamping my own formulation from an Einstein-de sitter exponentially decelerating universe to

a q = -1 accelerating universe in 1998, I found rho = (3/R)(kgm/meter^2). When substituted into the above equation, the expressions for G are the same (both subject to the 5/6 correction required to convert from a two sphere to a three sphere G field as previous repeated).

Page 7 of Chapter I, Cosmodynamics.pdf

Edited July 23, 2014 by cosnut

[cosnut]

This is a follow-up to Post 18, specifically a derivation of the G field based upon Mach's principle. Attached are two pages which illustrate the G field derived from cosmic mass content yields the same result as the G field derived from an accelerating empty space formalism. That the two are equal can be interpreted in several ways - the view taken in the Cosmodynamic Thesis is that the matter field is a consequence of spatial acceleration that leads to equal and opposite forces - consequently the net kinetic result is a coasting universe (q = 0). Even though empty space is accelerating - matter flux is net 'c'

 

Interested readers please see attached pages

Chapter III PP 55-57.pdf

[cosnut]

Time, Space and Gravitation have no separate existence from matter

 

Epistemologically, Einstein's one sentence description of GR is the operative medicament for a changing matter-changing G universe. Hubble's disposition of the static universe should have freed cosmology from the bondage of an invariant G and fixed inertial mass. The problem with limiting the allowable change in G to be less than what would be disclosed by the accuracy of the experiments is that the experiments are measuring MG. Once one of the factors such as G is considered fixed, then M follows - and the options for modeling a universe are severely limited. An evolving cosmos must accommodate at some early era, a whole lot of inertial mass in a short amount of time, to explain forever-after a fixed G, fixed mass evolutionary structure

 

So to make things work an inflation epoch is introduced, very high expansion velocities are required to comport with models based upon LCDM, the expansion velocity decreases due to G, then without explanation resumes.

 

What is elegant about the "Dirac G/Mach mass" universe is that no fine tuning is required - no requirement to separately adjust the ratio between G and M because one derives from the other - the universe always appears to have critical density.

 

The big problem is that the only experiments that could support the "Dirac G/Mach mass" universe are those already discussed (the Faint Sun paradox and the 1a Supernova). To interpret the latter as the result of varying G, would shake up a few people.

Edited July 24, 2014 by cosnut

[hypervalent_iodine]

!

Moderator Note

Moved to Speculations.

[Mordred]

a large part of my problem with this model is some of the terminology and definitions your using, for example false vacuum is a higher energy-density state than the true vacuum so when you use the term false vacuum one expects to see a correlation to the mexican hat potential of inflation.

 

in this article

Attached File Chapter III PP 55-57.pdf the use of pseudo space is well quite frankly meaningless, You limit the universe to the Hubble sphere where the universe is much larger than the Hubble sphere, then apply your metrics to Hubble sphere and state that anything beyond the Hubble sphere is unobservable, however this is incorrect. It would be better if you include the cosmological event horizon ( if I was a fresh brand new reader, I would immediately think this model is outdated, as the older models used to think the universe was restricted by the Hubble sphere)(we now know this isn't true), which brings me to the next problem how does your model with 3c recessive velocity? which is found at z=1090? Your going to need to apply correct correlations to today's cosmological understanding not the outdated older definitions.

 

 

in all honesty you may get a better audience if you take the time to look at how your defining and writing your descriptive's. Just a side not

 

The big problem is that the only experiments that could support the "Dirac G/Mach mass" universe are those already discussed (the Faint Sun paradox and the 1a Supernova). To interpret the latter as the result of varying G, would shake up a few people.

 

 

It would I agree however as any model requires supportive evidence these are the types of papers and studies you will need to support your paper no theory is complete without outside datum.

 

you haven't shown your full paper but if you look over any proposed alternative models they always include correlations to well known models in terms of comparison metrics, You never see a peer reviewed paper or at least I haven't without those comparisons. I'v studied more alternate models than I can reasonably estimate in all the time I've been interested in cosmology and reading peer reviewed papers. Such examples include MOND TEVES,Spin and torsion, Godel metric, Einstein cartan, F® gravity,Hl gravity etc, any of the peer reviewed papers always compare itself to the FLRW metrics and the Einstein field equations.

 

In your case I would be interested in how you define the stress energy tenser of the Einstein field equations? in comparison to your model how is it different how do I adapt the Einstein field equations to your model?

Edited July 24, 2014 by Mordred